Suppose y is a random sample of size n = 1 from a gamma distribution with parameters α = 1 and arbitrary β.
a. Show that 2y/β has a gamma distribution with parameters α = 1 and β = 2.
b. Use the result of part a to show that 2y/β has a chi square distribution with 2 degrees of freedom.
c. Derive a 95% confidence interval for b using 2y/β as a pivotal statistic.